I'm editing another photographer's wedding on my computer, through LR6. She has LR5. If I upgrade the existing LR5 catalog (I began edits on her computer), will I then be able to transfer my ratings and edits BACK on to her LR5 catalog of the same files, once I'm finished?

You can write the metadata to XMP in Lightroom 6, and then in Lightroom 5 read the metadata. Some edits will not transfer to Lightroom 5 if the specific edit did not exist in LR 5, but the rest of the edits will transfer.

You can't do this via transferring catalog files, if one person has an earlier version of Lightroom.